A117380 Riordan array (1/(1-4*x*c(x)),xc(x)), c(x) the g.f. of A000108.

1, 4, 1, 20, 5, 1, 104, 26, 6, 1, 548, 137, 33, 7, 1, 2904, 726, 178, 41, 8, 1, 15432, 3858, 954, 228, 50, 9, 1, 82128, 20532, 5100, 1242, 288, 60, 10, 1, 437444, 109361, 27233, 6701, 1601, 359, 71, 11, 1, 2331128, 582782, 145338, 35977, 8744, 2043, 442, 83, 12

Offset

0,2

Comments

Triangle factors as (1,xc(x))*(1/(1-4x),x). Inverse of A117377. First row is A076035. Second row is A076025(n)-0^n. Row sums are A076025(n+1). Diagonal sums are A117381.

Links

Table of n, a(n) for n=0..53.

Formula

Number triangle T(0,0)=1, T(n,k)=[k<=n]*sum{j=0..n, (j/(n-j))*C(2n-j,n-j)[k<=j]*4^(j-k)}

Example

Triangle begins
1,
4, 1,
20, 5, 1,
104, 26, 6, 1,
548, 137, 33, 7, 1,
2904, 726, 178, 41, 8, 1
Production array begins
4, 1
4, 1, 1
4, 1, 1, 1
4, 1, 1, 1, 1
4, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1, 1, 1
... - Philippe Deléham, Mar 05 2013

Crossrefs

Sequence in context: A128041 A144885 A144886 * A185420 A167432 A201639

Adjacent sequences: A117377 A117378 A117379 * A117381 A117382 A117383

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 10 2006

Status

approved